PSAT Math Grid-Ins Question 112: Answer and Explanation

Question: 112

A cafe sells drink vouchers for a private event. A voucher for one drink costs $6 and a voucher for two drinks costs $10. A total of 89 drinks were purchased with vouchers, and the voucher sales total was $462. What is the total number of vouchers that were sold?

Correct Answer: 53

Explanation:

53

The question asks for the total number of vouchers sold based on the cost of each voucher, the total voucher sales, and the total number of drinks sold. Translate the question in bite-sized pieces and write a system of equations for the situation. Use x to represent the number of vouchers sold for 1 drink and y to represent the number of vouchers sold for 2 drinks. One piece of information says that a voucher for 1 drink costs $6, so the sales for vouchers for 1 drink would be represented as 6x. The question states that a voucher for 2 drinks costs $10, so the sales for vouchers for 2 drinks would be represented as 10y. The question also states that the voucher sales total was $462, so 6x + 10y = 462. The question states that 89 drinks were purchased with vouchers. Each voucher represented as x is for 1 drink and each voucher represented as y is for 2 drinks, so the equation to represent the total number of drinks is x + 2y = 89. Solve the system of equations by stacking. Multiply the second equation by –6 and add it to the first equation to eliminate the x variable.

The result is –2y = –72. Divide both sides by –2 to get y = 36. Plug y back into either equation to solve for x. The second equation becomes x + 2(36) = 89, or x + 72 = 89. Subtract 72 from both sides to get x = 17. The total number of vouchers sold, or x + y, is 17 + 36 = 53. The correct answer is 53.